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Abstrakty
Let ω ∈ βN \ N be a free ultrafilter on N. It is known that there is a difficulty in constructing the ultrapower of unbounded operators. Krupa and Zawisza gave a rigorous definition of the ultrapower Aω of a self-adjoint operator A. In this note, we give an alternative description of Aω and the Hilbert space H(A) on which Aω is densely defined. This provides a criterion to determine a representing sequence (ξn)n of a given vector ξ ∈ dom(Aω) which has the property that Aωξ = (Aξn)ω holds. An explicit core for Aω is also described.
Słowa kluczowe
Czasopismo
Rocznik
Tom
Strony
147--159
Opis fizyczny
Bibliogr. 7 poz.
Twórcy
autor
- Institut des Hautes Études Scientifiques, Le Bois-Marie 35, route de Chartres, 91440 Bures-sur-Yvette, France
autor
- Nagahama Institute of Bio-Science and Technology, Nagahama 526-0829, Japan
autor
- Research Institute for Mathematical Sciences, Kyoto University, Sakyo-ku, Kitashirakawa Oiwakecho, 606-8502 Kyoto, Japan
Bibliografia
- [1] H. Ando and U. Haagerup, Ultraproducts of von Neumann algebras, arXiv: 12112.5457v2.
- [2] A. Kishimoto, Rohlin property for flows, Contemp. Math. 335 (2003), pp. 195-207.
- [3] A. Krupa and B. Zawisza, Applications of ultrapowers in analysis of unbounded selfadjoint operators, Bull. Polish Acad. Sci. Math. 32 (1984), pp. 581-588.
- [4] A. Krupa and B. Zawisza, Ultrapowers of unbounded selfadjoint operators, Studia Math. 87 (2) (1987), pp. 101-120.
- [5] T. Masuda and R. Tomatsu, Rohlin flows on von Neumann algebras, preprint, arXiv: 1206.0955v2.
- [6] H. Saigo, Categorical non-standard analysis, preprint, arXiv: 1009.0234.
- [7] K. Schmüdgen, Unbounded self-adjoint operators on Hilbert space, Grad. Texts in Math., Springer, 2012.
Uwagi
Opracowanie rekordu w ramach umowy 509/P-DUN/2018 ze środków MNiSW przeznaczonych na działalność upowszechniającą naukę (2019).
Typ dokumentu
Bibliografia
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